On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold

Details On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold On quasi-invariant transverse measures for the horospherical foliation of a negatively curved manifold

2002-07-04

arxiv.org/abs/math/0207043v1

Mathematics

Dynamical Systems

28 pages, 6 figures

Scientific paper

If $M$ is a compact or convex-cocompact negatively curved manifold, we associate to any Gibbs measure on $\tm$ a quasi-invariant transverse measure for the horospherical foliation, and prove that this measure is uniquely determined by its Radon-Nikodym cocycle. (This extends the Bowen-Marcus unique ergodicity result for this foliation.) We shall also prove equidistribution properties for the leaves of the foliation w.r.t. these Gibbs measures. We use these results in the study of invaiant meausres for horospherical foliations on regular covers of $M$.

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